ZAN Controller described probable multiple airspace incursion events resulting from several discussions taking place at the sector; all causing distractions.

Narrative

I took over the sector and there was already a D-Side trainee monitoring the sector; plugged in at the same position. The CIC notified me that the Non-RADAR separation standard ZOA was using on a flex track affecting my sector had increased from 25 miles either side of center line to 50 miles. We began discussing the impact and how to determine where I needed to apply increased separation. The D-Side trainee was asking a lot of questions about it as I was attempting to plot the flex track and protected airspace on the overhead map; and the CIC and I were discussing the difference between RADAR and Non-RADAR traffic in my sector on airway B327. When I returned my attention to the RADAR display I saw that Air Carrier X had progressed to KATCH without a hand-off to Vancouver Center and Air Carrier Y was about to enter Sector 69 without a hand-off as well. I immediately put Air Carrier Y into hand off mode and called over to the Sector 69 controller who said 'RADAR contact' as Air Carrier Y crossed the sector boundary. I called Vancouver on the shout line and gave them a hand off on Air Carrier X and another aircraft that was still in my sector. I apologized for the late hand-off and he said 'no problem.' I believe the primary cause of this error to be the combined distractions of the trainee and the CIC; and of course; my poor prioritizing of duties and inattention to my primary function; which is to watch the aircraft on the RADAR display and take action in a timely manner. Recommendation; when a CIC or FLM has something like this to communicate; they should be more aware of the distraction they can cause. If the sector is one-armed; maybe the CIC/FLM should do the plotting or whatever needs to be done instead of letting the Controller do it. In any case; someone should be monitoring the traffic at all times; or at least scan to see what is coming up in the next couple of minutes and take care of things before addressing the distracting issue. If a trainee is monitoring a sector; they should take care to avoid distracting the Controller; or assist in scanning the display for needed actions.